scholarly journals Deformation of a cantilever curved beam with variable cross section

2021 ◽  
Vol 16 (1) ◽  
pp. 23-36
Author(s):  
István Escedi ◽  
Attila Baksa
Keyword(s):  
Cross Section ◽  
Elastic Beam ◽  
Beam Theory ◽  
Variable Cross Section ◽  
The Other ◽  
Curved Beam ◽  
Variable Cross ◽  
Cross Sectional ◽  
Euler Bernoulli Beam

This paper deals with the determination of the displacements and stresses in a curved cantilever beam. The considered curved beam has circular centerline and the thickness of its cross section depends on the circumferential coordinate. The kinematics of Euler-Bernoulli beam theory are used. The curved elastic beam is fixed at one end and on the other end is subjected to concentrated moment and force; three different loading cases are considered. The paper gives analytical solutions for radial and circumferential displacements and cross-sectional rotation and circumferential stresses. The presented examples can be used as benchmark for the other types of solutions as given in this paper.

scholarly journals Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation

2019 ◽  
Vol 6 (1) ◽  
pp. 132-145 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Differential Quadrature Method ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Winkler Elastic Foundation ◽  
The Cross ◽  
Euler Bernoulli Beam

AbstractThis article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.

scholarly journals Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

2018 ◽  
Vol 30 (1) ◽  
pp. 82-99 ◽  
Author(s):  
Xuan Ling Zhang ◽  
Xiao Chao Chen ◽  
Echuan Yang ◽  
Hai Feng Li ◽  
Jian Bo Liu ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Electric Potential ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Beam ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Cross Sectional ◽  
Closed Form Solutions

In this article, closed-form solutions are obtained for vibrations of a magneto-electro-elastic beam with variable cross section. Based on Timoshenko beam assumptions, governing equation for the non-uniform beam with exponentially varying width is obtained. Laplace transform approach applied to the governing equation results in the corresponding Green’s functions for the beams with various boundary conditions. The equations, which are solved to obtain Green’s functions, are degenerated for the analyses of the characters of free vibration. For free vibrations of the beams under different mechanical boundary conditions, the effects of the non-uniformly cross-sectional parameters and magneto-electric boundary conditions on the dynamic characters are studied. In addition, the magneto-electric potential modal variables’ distributions through the thickness are presented. In the discussions of forced vibration, two points in the beam are selected to investigate frequency responses in terms of displacement and magneto-electric potential. Moreover, the influences of excitation frequency and cross-sectional parameter on through-the-thickness distributions of electric potentials are investigated.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

Geometrical Model for Permeable Material’s Porous Structure

2019 ◽  
Vol 7 (2) ◽  
pp. 42-54 ◽  
Author(s):  
А. Синцов ◽  
A. Sintsov ◽  
Владимир Девисилов ◽  
Vladimir Devisilov
Keyword(s):  
Porous Material ◽  
Porous Structure ◽  
Cross Section ◽  
Structural Characteristics ◽  
Variable Cross Section ◽  
Geometrical Model ◽  
Variable Cross ◽  
Experimental Stand ◽  
Experimental Technology

In this paper have been presented a new model of the porous structure, as well as an analysis of possibilities of a new method for experimental investigation of porous permeable materials and determination of their structural characteristics. An analysis for the majority of used in analytical calculations geometric models for a porous medium has been presented, and a model for a porous material in the form of porous matrix’s elementary cells has been proposed. Each of the cells contains a capillary channel with a variable cross-section. Volumetric structural characteristics, as well as dependencies of surface structural characteristics over the porous matrix’s thickness, are identical to these parameters, which have been obtained during the experimental study of a porous material. As a result of use of an original experimental technology offered by authors, and of experiment processing the porous matrix’s structure can be completely defined. The problem of creating an experimental setup, allowing determine the porous matrix’s characteristics, has been formulated. One of possible options for the experimental stand has been considered.

scholarly journals Theoretical and Experimental Research of The Stability of The Eccentrically Loaded Steel Columns with Variable Cross–Section

2018 ◽  
Vol 7 (3.2) ◽  
pp. 458
Author(s):  
Gennady Trusov ◽  
Vladimir Ruban
Keyword(s):  
Cross Section ◽  
Research Work ◽  
Variable Cross Section ◽  
Suggested Method ◽  
National Standards ◽  
Discrete Models ◽  
Practical Calculation ◽  
Variable Cross ◽  
Cross Sectional ◽  
Steel Columns

The article deals with the problem of determining the ultimate load for the eccentrically loaded steel columns with variable-cross section.The purpose of the research work is to offer an evaluation technique and practical calculation of load-bearing ability of the beam-columns with variable cross-section on the basis of numerical research, which will allow to consider the true form of element deflection curve, the effect of cross-section form, physical nonlinearity of the material, and variety of element boundary conditions. The distinctive characteristic of the suggested method is usage of the discrete models for cross-sectional parts, for the true stress-strain curves of the materials, and for the other input data. The method was tested and the results were compared to known theoretical solutions and national standards. To establish the reliability of the developed method, the experimental study of steel columns with variable cross-section was conducted. The suggested method allows to obtain column curves tables of lowering coefficients for these elements, that can be used in practice of civil engineering, and are convenient with national standards and Eurocode. 

The Changes of Internal Forces and the Reliability of Curved Bridge Taking the Cross-Sectional Design of Axial Symmetrical

2014 ◽  
Vol 587-589 ◽  
pp. 1631-1636
Author(s):  
Zheng Jiu Zhao ◽  
Jing Hong Gao
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Radius Of Curvature ◽  
Variable Cross ◽  
Cross Sectional ◽  
Box Girder ◽  
Curved Bridge ◽  
The Cross ◽  
Cross Sectional Design ◽  
Bridge Models

Taking a bridge of 160m long variable cross-section prestressed continuous curved box-girder as the research object and analyzing the cross-sectional design of axis with axial symmetrical or axial non-symmetrical to research the structure forces change of the upper part of bridge in different curvature. In order to test and verify the variable cross-section of prestressed continuous curved box-girder bridge is safe and reliable via cross-sectional design with axial symmetrical instead of axial non-symtrical within a radius of curvature of the interval. Creating the straight bridge and curved bridge models with different radius of curvature in same span by Midas/Civil to compare their structure forces.

Solar Concentrator Structural Optimization: A Variable Beam Cross Section Design

2017 ◽  
Author(s):  
Moucun Yang ◽  
Yuezhao Zhu ◽  
Wei Fu ◽  
Garth Pearce ◽  
Robert A. Taylor
Keyword(s):  
Structural Optimization ◽  
Cross Section ◽  
Cost Savings ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Maximum Displacement ◽  
Cross Sectional ◽  
Optical Efficiency ◽  
Box Structure ◽  
Section Design

The design and construction of solar concentrators heavily affects their cost, heat utilization and optical efficiency. Current trough concentrators support the reflector with an equivalent uniform beam configured from a metal grid sub-structure. Under gravity and wind loads, the support-structure stress distribution varies as a function of position of the structure and the tracking angle. In the conventional design, there is ample surplus stiffness and strength designed into some beams of the structure, which increases the overall weight and cost of the structure. This paper describes an approach towards structural optimization of trough concentrators (with the Eurotrough design taken as an example, that means that the safety factors and structure is similar with Eurotrough design) using a variable cross section beam. The main improvement of this approach comes from keeping the beams rigid and strong near the two ends (at the torque box structure) while allowing the middle of the structure to be relatively weak. Reducing the cross-sectional area of the central beams not only reduces amount of material needed for the structure but also reduces the deflection of the reflector. The simulated results show that the concentrator’s structural weight (including the torque box, endplates and cantilever arms) and the maximum displacement of the reflector are reduced about 15.3% (about 151.2kg per 12-metre long element) and 15.5%, respectively. This represents a meaningful capital and installation cost savings while at the same time improving the optical efficiency.

scholarly journals A well-balanced solver for the Saint Venant equations with variable cross-section

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Raul Borsche
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Variable Cross Section ◽  
Test Cases ◽  
Variable Cross ◽  
Bottom Slope ◽  
Cross Sectional ◽  
Analytical Properties ◽  
Saint Venant Equations ◽  
Numerical Solver

AbstractIn this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable cross-sectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation awell-balanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states.

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